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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) International Journal of Advances in Intelligent Informatics Indonesian Journal of Combinatorics
Suhadi Wido Saputro
Institut Teknologi Bandung
Computer Science & IT Decision Sciences, Operations Research & Management Electrical & Electronics Engineering

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The strong 3-rainbow index of edge-comb product of a path and a connected graph Zata Yumni Awanis; A.N.M. Salman; Suhadi Wido Saputro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.1.3

Abstract

Let G be a connected and edge-colored graph of order n, where adjacent edges may be colored the same. A tree in G is a rainbow tree if all of its edges have distinct colors. Let k be an integer with 2 ≤ k ≤ n. The minimum number of colors needed in an edge coloring of G such that there exists a rainbow tree connecting S with minimum size for every k-subset S of V(G) is called the strong k-rainbow index of G, denoted by srxk(G). In this paper, we study the srx3 of edge-comb product of a path and a connected graph, denoted by Pno⊳eH. It is clearly that |E(Pno⊳eH)| is the trivial upper bound for srx3(Pno⊳eH). Therefore, in this paper, we first characterize connected graphs H with srx3(Pno⊳eH)=|E(Pno⊳eH)|, then provide a sharp upper bound for srx3(Pno⊳eH) where srx3(Pno⊳eH)≠|E(Pno⊳eH)|. We also provide the exact value of srx3(Pno⊳eH) for some connected graphs H.
Adjusting cyber insurance premiums based on frequency in a communication network Sapto Wahyu Indratno; Yeftanus Antonio; Suhadi Wido Saputro
International Journal of Advances in Intelligent Informatics Vol 7, No 3 (2021): November 2021
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26555/ijain.v7i3.698

Abstract

This study compares cyber insurance premiums with and without a communication network effect frequency. As a cybersecurity factor, the frequency in a communication network influences the speed of cyberattack transmission. It means that a network or a high activity node is more vulnerable than a network with low activity. Traditionally, cyber insurance pricing considers historical data to set premiums or rates. Conversely, the network security level can evaluate using the Monte Carlo simulation based on the epidemic model. This simulation requires spreading parameters, such as infection rate, recovery rate, and self-infection rate. Our idea is to modify the infection rate as a function of the frequency in a communication network. The node-based model uses probability distributions for the communication mechanism to generate the data. It adopts the co-purchase network formation in market basket analysis for building weighted edges and nodes. Simulations are used to compare the initial and modified infection rates. This paper considered prism and Petersen graph topology as case studies. The relative difference is a metric to compare the significance of premium adjustment. The results show that the premium for a node with a low level in a communication network can reach 28.28% lower than the initial premium. The premium can reach 20.99% lower than the initial network premium for a network. Based on these results, insurance companies can adjust cyber insurance premiums based on computer usage to offer a more appropriate price.
On size multipartite Ramsey numbers for stars Anie Lusiani; Edy Tri Baskoro; Suhadi Wido Saputro
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (322.917 KB) | DOI: 10.19184/ijc.2019.3.2.4

Abstract

Burger and Vuuren defined the size multipartite Ramsey number for a pair of complete, balanced, multipartite graphs mj(Kaxb,Kcxd), for natural numbers a,b,c,d and j, where a,c >= 2, in 2004. They have also determined the necessary and sufficient conditions for the existence of size multipartite Ramsey numbers mj(Kaxb,Kcxd). Syafrizal et al. generalized this definition by removing the completeness requirement. For simple graphs G and H, they defined the size multipartite Ramsey number mj(G,H) as the smallest natural number t such that any red-blue coloring on the edges of Kjxt contains a red G or a blue H as a subgraph. In this paper, we determine the necessary and sufficient conditions for the existence of multipartite Ramsey numbers mj(G,H), where both G and H are non complete graphs. Furthermore, we determine the exact values of the size multipartite Ramsey numbers mj(K1,m, K1,n) for all integers m,n >= 1 and j = 2,3, where K1,m is a star of order m+1. In addition, we also determine the lower bound of m3(kK1,m, C3), where kK1,m is a disjoint union of k copies of a star K1,m and C3 is a cycle of order 3.
The local metric dimension of split and unicyclic graphs Dinny Fitriani; Anisa Rarasati; Suhadi Wido Saputro; Edy Tri Baskoro
Indonesian Journal of Combinatorics Vol 6, No 1 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.1.3

Abstract

A set W is called a local resolving set of G if the distance of u and v to some elements of W are distinct for every two adjacent vertices u and v in G.  The local metric dimension of G is the minimum cardinality of a local resolving set of G.  A connected graph G is called a split graph if V(G) can be partitioned into two subsets V1 and V2 where an induced subgraph of G by V1 and V2 is a complete graph and an independent set, respectively.  We also consider a graph, namely the unicyclic graph which is a connected graph containing exactly one cycle.  In this paper, we provide a general sharp bounds of local metric dimension of split graph.  We also determine an exact value of local metric dimension of any unicyclic graphs.
Co-Authors A.N.M. Salman Anisa Rarasati Debi Oktia Haryeni Dinny Fitriani Edy Tri Baskoro Lusiani, Anie Sapto Wahyu Indratno Yeftanus Antonio Zata Yumni Awanis